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  2. Hermite's problem - Wikipedia

    en.wikipedia.org/wiki/Hermite's_problem

    The real number x is a rational number only if its decimal expansion is eventually periodic, that is if there are natural numbers N and p such that for every n ≥ N it is the case that a n+p = a n. Another way of expressing numbers is to write them as simple continued fractions, as in: = [;,,, …], where a 0 is an integer and a 1, a 2, a 3 ...

  3. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...

  4. Irrational number - Wikipedia

    en.wikipedia.org/wiki/Irrational_number

    In constructive mathematics, excluded middle is not valid, so it is not true that every real number is rational or irrational. Thus, the notion of an irrational number bifurcates into multiple distinct notions. One could take the traditional definition of an irrational number as a real number that is not rational. [35]

  5. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Even and odd numbers: An integer is even if it is a multiple of 2, and is odd otherwise. Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...

  6. Niven's theorem - Wikipedia

    en.wikipedia.org/wiki/Niven's_theorem

    In radians, one would require that 0° ≤ x ≤ π/2, that x/π be rational, and that sin(x) be rational. The conclusion is then that the only such values are sin(0) = 0, sin(π/6) = 1/2, and sin(π/2) = 1. The theorem appears as Corollary 3.12 in Niven's book on irrational numbers. [2] The theorem extends to the other trigonometric functions ...

  7. Ágnes Keleti, oldest living Olympic medal winner and ...

    www.aol.com/gnes-keleti-oldest-living-olympic...

    Ágnes Keleti, the oldest living Olympic medalist and Holocaust survivor died in Budapest, Hungary on Thursday.

  8. Boardroom diversity stalls amid DEI backlash. Could that ...

    www.aol.com/boardroom-diversity-stalls-amid-dei...

    Among Russell 3000 companies, the number of new Black directors fell to 12% in 2024 from 26% two years ago, according to the study by business research group the Conference Board and data firm ...

  9. Irrationality measure - Wikipedia

    en.wikipedia.org/wiki/Irrationality_measure

    Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...